Properties

Label 350.3.l
Level $350$
Weight $3$
Character orbit 350.l
Rep. character $\chi_{350}(69,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $160$
Newform subspaces $1$
Sturm bound $180$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 350.l (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 175 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(180\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(350, [\chi])\).

Total New Old
Modular forms 496 160 336
Cusp forms 464 160 304
Eisenstein series 32 0 32

Trace form

\( 160 q + 80 q^{4} - 120 q^{9} + O(q^{10}) \) \( 160 q + 80 q^{4} - 120 q^{9} - 60 q^{11} - 44 q^{15} - 160 q^{16} - 60 q^{21} + 40 q^{22} + 100 q^{23} + 40 q^{28} - 60 q^{29} - 16 q^{30} + 58 q^{35} + 240 q^{36} - 320 q^{39} + 120 q^{42} - 80 q^{44} + 120 q^{46} + 140 q^{49} - 192 q^{50} + 240 q^{51} - 60 q^{53} - 232 q^{60} + 100 q^{63} + 320 q^{64} + 292 q^{65} - 156 q^{70} + 460 q^{71} + 160 q^{74} - 240 q^{77} - 440 q^{79} + 80 q^{81} - 180 q^{84} - 912 q^{85} + 240 q^{86} + 320 q^{88} + 200 q^{91} + 240 q^{92} + 596 q^{95} - 160 q^{98} + 760 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(350, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
350.3.l.a 350.l 175.m $160$ $9.537$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{3}^{\mathrm{old}}(350, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(350, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)